Light - Reflection and Refraction
CHAPTER – 10
LIGHT-REFLECTION
& REFRACTION
Light is a form of energy, which enable us to see the object.
In this chapter we will study the phenomena of reflection and refraction using the
property of light i.e. straight line propagation (Light wave travel from one point to
another, along a straight line).
Reflection of Light
When the light is allowed to fall on highly polished surface, such as mirror, most of
the light gets reflected.
normal
Laws of Reflection
1.
2.
The angle of incidence is always equal to
angle of reflection.
—
i=—
r
The incident ray, reflected ray and the
normal to the reflecting surface at the
point of incidence lie in the same plane.
Reflected
ray
Incident
ray
i
r
Points of incidences
Image formed by Plane Mirror (Plane reflecting surface)
Plane Mirror
A1
A
Object
B
Image
—
i
—
r
B1
1)
Virtual (imaginary) & Erect (Virtual
screen.)
2)
Laterally inverted (The left side of object appear on right side of image)
3)
The size of image is equal to that of object
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The image that do not form on
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Light - Reflection and Refraction
4.
The image formed is as for behind the mirror as the object is in front of it.
Reflection of light by spherical Mirrors
Mirrors, whose reflecting surface are curved inward or outward spherically are
called spherical mirror.
For example - Spoon } fi
The curved surface of shinning spoon can be considered
as curved mirror.
If it is curved inward fi
Act as concave mirror
If it is curved outward fi
Act as a convex mirror.
Reflecting
side
Reflecting
side
Concave
Mirror
OR CONVERGING
MIRROR
Convex
mirror
OR DIVERGING
MIRROR
Few Basic terms related to Spherical Mirror
Principal
Axis
Radius of curvature
R
F
f
focal length
C
Principal
Axis
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Concave
Mirror
P
Radius of curvature
R
P
f
F
focal length
Convex
Mirror
C
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Light - Reflection and Refraction
1.
Principal axis : Line joining the pole and centre of curvature of the spherical
mirror.
2.
Pole : The geometrical central point of the reflecting spherical surface.
(aperture), denoted by (P).
3.
Aperture : The width of reflecting spherical surface.
4.
Centre of curvature : The reflecting surface of a spherical mirror form a part
of sphere. It has a centre, which is known as centre of curvature, denoted by
(C)
5.
Radius of curvature : The separation between the pole and the centre of
curvature. ie. PC = R
6.
Focus point : The point on the principal axis, where all parallel rays meet
after reflection, denoted by (F)
7.
Focal length : The length between the pole and focus point i.e. PF = f
8.
Relationship between focal length and Radius of curvature.
F= R
2
Image formation by spherical Mirror
Before we learn the formation of image or ray diagram, let us go through few tips
a)
Remember, A say of light which is parallel to principle axis always pass
through focus (meet at focus) or vice-versa
P
Principal
Axis
C
P
Principal C
Axis
F
F
CONCAVE
MIRROR
CONCAVE
MIRROR
Principal
Axis
P
F
C
CONVEX MIRROR
Appear as if coming
from focus pt in case of convex mirror
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Light - Reflection and Refraction
Principal
Axis
b)
P
C
F
A ray of light which passes through centre of curvature (it is also known as
normal at the point of incidence on spherical mirror) will retrace their path
after reflection
Pole (P)
Principal
Axis
F
C
CONCAVE
MIRROR
P
Principal
Axis
c)
F
C
CONVEX
MIRROR
A ray of light falling on pole get reflected at the same angle on the other side of
principal axis.
i
C
P
F
—
i
—
r
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—
i=—
r
r
—
i=—
r
F
C
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Light - Reflection and Refraction
Note : A ray of light passes through centre of cus-valerie reflecting spherical
surface is always act as normal at the point of incidence. If we know the normal we
can draw angle of incidence and angle of reflection
i
r
ng
(passi c)
h
g
u
o
r
th
C
al
norm dence
inci
f
o
t
p
t
P
F
a
—
r
—
i
P
F
C
Note : The image will only form when two or more rays meets at apoint. Image
formation by a concave mirror for different position of the object
1.
Object
At infinity
Position of
Image
At focus
P
C
2.
Object
Beyond C
F
Size of
Image
Highly diminished
(point size)
A
object
B
B1
P
F
C image
—
i
—
r
Object
At C
A
B1 B
P
F
A
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Position of
Image
Between F&C
Nature
Real and
Inverted
Size of
Image
Small
A1
3.
Nature
Real and
Inverted
Position of
Image
At C
Nature
Real and
Inverted
Size of
Image
Same Size
of object
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Light - Reflection and Refraction
4.
Object
Between C&F
—
i=—
r
Position of
Nature
—
i
Image
P
Real and
—
r
Beyond C
Inverted
A
Object
B1
B
C
F
Image
A
5.
Size of Image
Enlarged
1
Object
At F
A
B
C
F
—
i
P
—
r
—
i=—
r
Position of
Nature
Image
Real and
At (infinity)
Inverted
Size of Image
Highly enlarged
A1
6.
Object
Between F&P
(Special Case)
A
C
F
P
—
i
r
B —
B1
Position of Image
Behind the mirror
Size of Image
Enlarged
Nature
Virtual
and
Erect
Image formation by Convex Mirror
1.
Object
At infinity
P
F
Position of Image
At focus
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Size of Image
Highly diminished
C
Nature
Virtual & erect
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Light - Reflection and Refraction
1.
Object
Anywhere between
infinity and pole
of the mirror
A
A1
P
B
B1
Position of Image
Between P & F
Size of Image
Very small
F
Nature
Virtual & erect
Uses of Concave Mirror
1.
Used in torches, search light and headlight of vehicle.
2.
Used to see large image of face as shaving mirror
3.
Used by dentist to see large images of the teeth
4.
Large concave mirror used to focus sunlight (heat) in solar furnaces.
Uses of Convex Mirror
1.
Used as rear-view mirror in vehicles because it gives erect image. It also helps
the driver to view large area.
Sign Convention for Reflection by Spherical Mirror
1.
The object is always placed to the left side of mirror.
2.
All distance should be measured from pole (P); parallel to principal axis.
3.
Take 'P' as origin. Distances measured
Right of the origin (+ x - Axis) are taken positive
Left of the origin (– x-Axis) are taken negative
Perpendicular to and above principal axis (+y-Axis) are taken positive
Perpendicular to and below principal axis (–y-Axis) are taken negative
+y
o
–x
+x
(Cartesian system)
–y
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Light - Reflection and Refraction
MIRROR FORMULA
ffi
distance between F and Pole
vfi
distance of image from Pole
u fi
distance of object from Pole
Rfi
distance between centre of curvature and pole.
1
1
1
F = v + u
R
where f = 2
MAGNIFICATION
It is expressed as the ratio of the height of the image to height of the object
m=
height of image h1
=
height of object h
1
It is also related to 'u' and 'v'
–v
m= u
2
\
from 1 and 2 equation
m=
1
image height from principle axis
h1
– v where h fi
1
h fi
Object height from principle axis.
h = u
It magnitude m > 1 _____ Image is magnified
m = 1 _____ Image is of same size
m < 1 _____ Image is dimirushed
Few tips to remember sign convention for Spherical mirror
1
Object height h fi
always positive | Image height h
- negative
} Real
Virtual - positive
Object distance from pole u fi
is always negative
Image distance from pole
}
Real - Image
always negative
v fi
Virtual - Image always positive
}
Concave mirror – always negative
Focal length f fi
Convex mirror – always positive
REFRACTION OF LIGHT
Refraction of Light : Happens in Transparent medium when a light travels from
one medium to another, refraction takes place.
A ray of light bends as it moves from one medium to another
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Light - Reflection and Refraction
Refraction is due to change in the speed of light as it enters from one transparent
medium to another.
Speed of light decreases as the beam of light travel from rarer medium to the denser
medium.
normal
normal
Incident
Ray
Denser medium
Raver medium
Denser medium
Rarer medium
Refracted Ray
When ray travel from Rarer to Denser it bends When ray travel from denser to
towards normal after refraction
rarer medium it bends away
from normal
Some Commonly observed phenomenon due to Refraction
1.
The stone at the bottom of water tub appear to be raised.
2.
A fish kept in aquarium appear to be bigger than its actual size.
3.
A pencil partially immersed in water appears to be displaced at the interface of
air and water.
Refraction through a Rectangular Glass Slab
A
N
Incident ray
Air (Rarer Medium)
i1
K
L
O
r1
i2 N
N
Here light ray changes is
direction at O and O1, the
point at the interface of
transparent medium.
Glass
(Denser
Medium)
1
O
e
1
M
Air (Rarer Medium)
(Refracted Ray)
C
B
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Light - Reflection and Refraction
When a incident ray of light AO passes from a rarer medium (air) to a denser
medium (glass) at point. O on interface AB, it will bends towards the normal. At pt
O1, on interface DC the light ray entered from denser medium (glass) to rarer
medium (air) here the light ray will bend away from normal OO1is a refracted ray
OB is an emergent ray. If the incident ray is extended to C, we will observe that
emergent ray O1B is parallel to incident ray. The ray will slightly displaced laterally
after refraction.
Note : When a ray of light is incident normally to the interface of two media it will
go straight, without any deviation.
Laws of refraction of light1.
The incident ray, the refracted ray and the normal to the interface of two
transparent media at the point of incidence, all lie in the same plane.
2.
The ratio of sine of angle of incidence to the sine of angle of refraction is a
constant ie.
Sin i
constant
Sin r =
(r)
for given colour and pair of media, this law is also known as Snells Law
Constant n is the refractive index for a given pair of medium. It is the refractive
index of the second medium with respect to first medium.
n2
Sin i
Sin r = n1 = n21
Where 2 is for second
medium and 1 is for first
medium
Refractive Index
The refractive index of glass with respect is air is given by ratio of speed of light in
air to the speed of light in glass.
ng
Speed of light in air
c
nga = n =
= v
a
Speed of light in glass
C fi
Speed of light in vacuum = 3·
108 m/s
speed of light in air is marginally less, compared to that in vacuum.
Refractive index of air with respect to glass is given by
(
na
a fi
air
Speed of light in glass
v
nag = n =
= c
g fi
glass
g
Speed of light in air
)
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Light - Reflection and Refraction
The absolute refractive index of a medium is simply called refractive index
nm =
Speed of light in air
c
= v
Speed of light in the medium
Refractive index of water (nw) = 1.33
Refractive index of glass (ng) = 1.52
Spherical Lens
A transparent material bound by two surface, of which one or both surfaces are
spherical, forms a lens.
CONVEX LENS
A lens may have two spherical surfaces, bulging outwards, is
called double convex lens (or simply convex lens.
It is also known as converging lens because it converges the light.
CONCAVE LENS
A lens bounded by two spherical surfaces, curved inwards is
known as double concave lens (or simply concave lens)
It is also known as diverging lens because it diverges the light.
Few Basic Terms related to spherical lens.
R
Principal
Axis
C1
or (2F1)
f
O
F1
F2
Optical
centre (O)
R
Principal
Axis
C1
C2
or (2F2)
Optical centre (O)
O
F1
F2
C2
Convex
Lens
Concave
Lens
f
C1
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O
C2
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Light - Reflection and Refraction
1.
Centre of curvature - A lens, either a convex lens or a concave lens has two
spherical surfaces. Each of these surfaces form a part of sphere. The centre of
these two spheres are called centre of curvature represented by C1 and C2.
2.
Principal axis - Imaginary straight line passing through the two centres of
curvature
3.
Optical Centre - The central point of lens is its optical centre (O). A ray of
light, when passes through 'O' it remains undeviated i.e. it goes straight.
4.
Aperture - The effective diameter of the circular outline of a spherical lens.
5.
Focus of lens - Beam of light parallel is principal axis, after refraction from
1) Convex lens, converge to the point on principal axis, denoted by F,
known as Principal focus
Principal Axis
F1
O
F2
2) Concave lens, appear to diverge from a point on the principal axis, known
as principal focus.
O
F1
Principal
Axis
F2
The distance OF2 and OF1 is called as focal length
Tips for drawing Ray diagram
a)
After refraction, a ray parallel to principal axis will pass through F.
F1
O
(Converge)
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F2
F1
O
F2
Principal
Axis
(Diverge)
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Light - Reflection and Refraction
b)
A ray passes through F, after refraction will emerge parallel to principal axis.
F1
c)
F2
Principal
Axis
O
F2
F1
O
Principal
Axis
A ray passes through optical centre 'O', paeses without any deviation.
F1
F1
F2
O
O
F2
Principal
Axis
Image formation by a convex lens for various position of object
1.
Object
At infinity
2F1
2.
F1
F2
2F2
Object
Beyond 2F1
A
B1
B
2F1
F1
O
2F2
F2
Position of Image
At focus
F2
Size of Image
Highly
diminished
(point size)
Nature
Real &
inverted
Position of Image
Between F2 & 2F2
Nature
Real &
inverted
Size of Image
Small
A1
3.
Object
At 2F1
A
1
B
B
2F1
F1
O
F2
2F2
A1
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Position of Image
At 2F2
Size of Image
Same size of
object
Nature
Real &
inverted
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Light - Reflection and Refraction
4.
Position of Image
Beyond 2F2
Object
Between F1 & 2F1
A
Size of Image
Enlarged
B
2F1
F1
O
B1
2F2
F2
Nature
Real &
inverted
A1
5.
Object
At focus F1
Position of Image
at infinity
A
Size of Image
Highly Enlarged
B
2F1
6.
F1
O
(Special Case)
Object
Between F1 and
optical centre 'O'
Position of Image
On the same
side of the
object
F2
2F2
Size of Image
Enlarged
A1
A
2F1
F1 B
O
F2
2F2
Position of Image
At F1
Size of Image
Highly Diminished
F1
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Nature
Virtual &
Erect
B1
Image formation by concave lens
1.
Object
Alt infinity
2F1
Nature
Real &
inverted
O
F2
Nature
Virtual &
Erect
2F2
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Light - Reflection and Refraction
2.
Position of Image
Between F1 & O
Object
Between infinity
and optical centre
(at any point)
Size of Image
Very small
A
Nature
Virtual
& Erect
A
B
F1 B
2F1
F2
O
2F2
Sign Convention for Refraction by spherical lens
Similar to that of spherical mirror, only the difference is that all the measurement
are made from optical centre 'O'
+ y-axis
o
+ x-axis
– x-axis
– y-axis
LENS FORMULA
'O' fi
optical centre
f - distance between F and 'O'
u - distance of object from 'O'
v - distance of image from 'O'
r - distance between centre
of curvature & 'O'
1
1 – 1
=
f
v
u
f=
R
2
MAGNIFICATION
It is defined as the ratio of the height of image to the height of object.
m=
height of image
height of object
1
=
h
= 1
h
}
h1 – image height
from principal axis
h – object height
from principal axis
It is also related to 'u' & 'v'
m=
v
u
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Light - Reflection and Refraction
From equation 1 & 2
m=
h1
h
v
u
=
If magnitude of m > | fi
Image is magnified
m = 1 fi
Image is of same size
m < | fi
Image is deminished
Few tips to remember sign convention for spherical lens
Object height h
fi
is always positive
Image height h1
Realfi
is always negative
Virtualfi
is always positive
Object distance from optical centre u fi
is always negative
}
Realfi
positive
Image distance from optical centre v fi
virtual fi
negative
}
Convex lensfi
is always positive
Focal length v fi
Concave lensfi
is always negative
Power of Lens
The degree of convergence or divergence of light ray achieved by a lens is known
as power of a lens.
It is difined as the reciprocal of its focal length Represented by P
f=
1
f
It f is given in meter, then
1
P=
f
It f is given in cm, then
100
P=
f
SI unit of power of a lens is "dioptre" denoted by 'D'
I dioptre or ID fi
It is the power of lens whose focal length is 1m
1
–1
ID =
OR ID = 1m
1m
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Light - Reflection and Refraction
Power convex lens or converging lens is always positive
O
f is +ve
F2
Power of concave lens or diverging lens is always negative
f is –ve
F1
O
If any optical instrument have many lens, then net power will be
P = P1 + P2 + P3....
EXERCISE
(Question Bank)
Very Short Answers Type Questions (1 Mark)
1.
If the angle of incidence is O°, what is the angle of reflection?
2.
What is the nature of image formed by concave mirror if the magnification
produced by the mirror is +3?
3.
Give two uses of concave mirror?
4.
Find the focal length of a convex mirror, whose radius of curvature is 30 cm?
5.
What do you understand by magnification of a spherical mirror?
6.
An object is held at the principal focus of a concave lens of focal length f.
Where the image will form?
7.
Show the angle of incidence and angle of refection.
F
8.
Complete the ray diagram.
2F1
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F1
O
F2
2F2
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Light - Reflection and Refraction
9.
Define the SI unit of power of lens.
10.
When light undergoes refraction at the surface of seperation of two media,
what happens to speed of light.
Short Answer Type Questions (2-3 Marks)
1.
What do you understand by refraction of light. Draw the labelled ray
diagram, when ray passes through glass slab.
2.
The refractive index of glass is 1.54 and the speed of light in air is 3x108 m/s.
Calculate the speed of light in water?
3.
A convex mirror used on an automobile has a focal length of 6m. If vehicle
behind is at a distance of 12m. Find the nature and location of image.
(4m, virtual erect small)
4.
A concave lens of focal length 15cm, forms an image 10 cm from the lens.
How far is the object placed from the lens? Draw the ray diagram?
5.
Two thin lens of power +3.5D and - 2.5D are placed in contact. Find the
power and focal length, if the lens are in combination.
(p = + 10, f = 1m)
6.
What are the law of refraction. Define refractive index of a medium.
Very Long Answer Type Questions (5 Marks)
1.
2.
Draw the ray diagram, showing the image formed by concave mirror, when
object is placed at
a)
at infinity
b)
between F22F
c)
At 2F
d)
At F
e)
between F&P
Draw the ray diagram, showing the image formed by convex lens, when
object is placed at.
a)
At infinity
b)
between F1 & 2F1
c)
At 2F1
d)
Beyond 2F1
e)
between F1 & optical centre 'O'
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